Transmission efficiency of a line increases with

Question

Examoogle · Accepted Answer

Option B: Increase in power factor and voltage

Explanation & Concepts:
Transmission efficiency is the ratio of output power to input power at the receiving end of a transmission line. Increasing both the power factor and the operating voltage reduces the line current for a given power, thereby decreasing $I^2R$ losses and improving overall efficiency.

Working Principle: The transmission line power loss is proportional to $I^2 R$. By increasing the line voltage $V$, the current $I$ required to transmit a specific amount of power $P$ ($P = \sqrt{3}VI \cos \phi$) decreases significantly. Simultaneously, increasing the power factor $\cos \phi$ further reduces the current component, minimizing resistive power loss and voltage drop.

Key Formulas: $\eta = \frac{P_{out}}{P_{out} + I^2 R} 	imes 100\%$ — Definition of transmission efficiency; $I = \frac{P}{\sqrt{3} V \cos \phi}$ — Relationship between current, voltage, and power factor

Key Points: Efficiency is inversely proportional to line losses.; Higher voltage levels are preferred for long-distance power transmission to minimize line currents.; Power factor correction (e.g., using capacitor banks) improves the effective utilization of transmission line capacity.; Lower current reduces both copper losses and voltage regulation issues.

Advantages: Reduced $I^2 R$ transmission losses; Improved voltage regulation; Increased thermal capacity of conductors

Disadvantages: Higher insulation costs at elevated voltages; Potential for increased corona loss at high voltages

Applications: High Voltage Direct Current (HVDC) systems; EHV/UHV AC transmission grids

Additional Info: Transmission efficiency $\eta$ is defined as the ratio of power delivered at the load to the power sent from the source.. Option A is incorrect because decreasing voltage and power factor leads to higher currents and increased heat losses, reducing efficiency.

Answer: B is correct — Transmission efficiency improves when power factor and voltage increase because both actions serve to minimize the magnitude of line current, thereby reducing resistive power losses.

Exam Tip: Always remember that in power systems, higher voltage transmission is the most effective way to optimize efficiency and reduce conductor material requirements (Kelvin's Law).

Examoogle · Answer

Option A: Decrease in power factor and voltage

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Option C: Increase in power factor but decrease in voltage

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Option D: Increase in voltage but decrease in power factor

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